A109559 prime(k) for those k where floor((2*(prime(k+1)-prime(k))*PrimePi(k) mod (8*k))/k) = m with m = 5.

23, 31, 283, 337, 409, 421, 547, 577, 631, 661, 797, 997, 1201, 1237, 1307, 1459, 1499, 1511, 1531, 1583, 1709, 1789, 1811, 1889, 2039, 2357, 2423, 2633, 2753, 2819, 2939, 3023, 3593, 3677, 3779, 3833, 3863, 4057, 4111, 4139, 4493, 4567, 4621, 4817, 4889, 4973

Offset: 1

Author

Roger L. Bagula, Jun 27 2005

Keywords

• nonn
• less

Crossrefs

Cf. A000040, A000720, A001359.

Cf. A109556-A109569 for m = 2..15.

Programs

Mathematica

a = Flatten[Table[If[Floor[2*Mod[(Prime[n + 1] - Prime[n])*PrimePi[n]/n, 8]] == 5, Prime[n], {}], {n, 1, 400}]]

Extensions

Name edited, offset corrected and more terms added by Amiram Eldar, Jun 02 2025